分类： 数学 >> 应用数学 提交时间： 2021-09-22
摘要： In the early days of the epidemic of coronavirus disease 2019 (COVID-19), due to insufficient knowledge of the pandemic, inadequate nucleic acid tests, lack of timely data reporting, etc., the origin time of the onset of COVID-19 is difficult to determine. Therefore, source tracing is crucial for infectious disease prevention and control. The purpose of this paper is to infer the origin time of pandemic of COVID-19 based on a data and model hybrid driven method. We model the testing positive rate to fit its actual trend, and use the least squares estimation to obtain the optimal model parameters. Further, the kernel density estimation is applied to infer the origin time of pandemic given the specific confidence probability. By selecting 12 representative regions in the United States for analysis, the dates of the first infected case with 50% confidence probability are mostly between August and October 2019, which are earlier than the officially announced date of the first confirmed case in the United States on January 20, 2020. The experimental results indicate that the COVID-19 pandemic in the United States starts to spread around September 2019 with a high confidence probability. In addition, the existing confirmed cases are also used in Wuhan City and Zhejiang Province in China to infer the origin time of COVID-19 and provide the confidence probability. The results show that the spread of COVID-19 pandemic in China is likely to begin in late December 2019.
分类： 数学 >> 统计和概率 分类： 统计学 >> 数理统计学 分类： 信息科学与系统科学 >> 信息科学与系统科学基础学科 提交时间： 2024-04-11
摘要： 统计独立性是统计学和机器学习领域的基础性概念，如何表示和度量统计独立性是该领域的基本问题。Copula理论提供了统计相关关系表示的理论工具，而Copula熵理论则给出了度量统计独立性的概念工具。本文综述了Copula熵的理论和应用，概述了其基本概念定义、定理和性质，以及估计方法。介绍了Copula熵研究的最新进展，包括其在统计学的十个基本问题（结构学习、关联发现、变量选择、因果发现、系统辨识、时延估计、域自适应、正态性检验、双样本检验和变点检测等）上的理论应用。讨论了前四个理论应用之间的关系，以及其对应的深层次的相关性和因果性概念之间的联系，并将Copula熵的（条件）独立性度量框架与基于核函数和距离相关的同类框架进行了理论对比，又通过仿真和实际数据实验评估验证了Copula熵的实际优越性。简述了Copula熵在理论物理学、天体物理学、地球物理学、理论化学、化学信息学、材料学、水文学、气候学、气象学、环境学、生态学、动物形态学、农学、认知神经学、运动神经学、计算神经学、心理学、系统生物学、生物信息学、临床诊断学、老年医学、精神病学、公共卫生学、经济学、管理学、社会学、教育学、计算语言学、新闻传播学、法学、政治学、军事学、情报学，以及能源工程、食品工程、土木建筑、交通运输、制造工程、可靠性工程、冶金工程、化学工程、航空航天、兵器工程、车辆工程、电子工程、通信工程、高性能计算、信息安全、测绘遥感和金融工程等领域的实际应用。
分类： 数学 >> 数学（综合） 提交时间： 2018-09-22
摘要： Explicit equations are obtained to convert Cartesian coordinates to elliptic coordinates, based on which an elliptic-coordinate function can be readily mapped on a uniform Cartesian mesh.Application to Kirchhoff vortex is provided.
分类： 数学 >> 应用数学 分类： 管理学 >> 管理工程 分类： 信息科学与系统科学 >> 信息与系统科学其他学科 提交时间： 2020-03-31
摘要： 本文的目的是建立区块链生态系统中采矿池博弈共识均衡的一般框架，特别是在区块链生态系统中，通过使用一个新的概念“共识博弈（Consensus Game）”，解释与挖掘差距（Gap Games）博弈行为相关的共识均衡存在的意义上的稳定性，这里，区块链生态系统主要是指应用2008年中本聪（Nakamoto）所提出的“工作证明”(Proof of Work) 这一关键共识，将区块链工作的费用、报酬机制和采矿权三类不同因素考虑在内的经济活动。 为了做到这一点，我们首先概述了采矿池游戏共识均衡的一般存在性是如何表述的，然后通过区块链共识框架下共识均衡的存在性来解释比特币缺口博弈 (Gap博弈) 稳定性，然后利用博弈论中矿工的利润函数作为收益，建立了一般矿业缺口博弈一致均衡的一般存在性结果。作为应用，建立了缺口博弈 (Gap博弈)一致均衡的一般存在性结果，这不仅有助于我们在区块链生态系统的一般框架下断言缺口博弈 (Gap博弈) 的一般稳定性的存在性，但也让我们能够说明在研究采矿池博弈时的一些不同现象，这些现象可能是由于采矿者的(Gap博弈)行为与嵌入比特币经济学的情景造成的。 我们对区块链生态系统挖掘缺口博弈稳定性的解释研究表明，共识均衡的概念可能对共识经济学基础理论的发展起到重要作用
分类： 物理学 >> 电磁学、光学、声学、传热、经典力学和流体动力学 分类： 信息科学与系统科学 >> 信息科学与系统科学基础学科 分类： 数学 >> 数学（综合） 提交时间： 2017-11-26
摘要： 大气对红外辐射传输的影响引起的红外成像灰度变化，是红外目标跟踪应用需要应对的问题。本文的研究目的是对红外成像灰度变化规律进行李群建模，对设计高效、鲁棒的目标跟踪算法有重要意义。首先分析了红外辐射传输模型，并结合红外成像机理，得到红外成像灰度变化模型。进一步从理论上证明了大气影响下红外成像灰度变化规律符合李群结构，提出了红外图像灰度动态变化的一种非欧数学表征。最后根据红外成像灰度变化模型对不同环境下采集到的外场实验数据进行拟合，回归分析结果表明了该模型的准确性，进而说明了本文对红外成像灰度变化规律进行李群表达的合理性。
分类： 数学 >> 数学（综合） 提交时间： 2017-06-22
摘要： 考虑股票选取的多因子问题，在传统模型的基础上，利用MATLAB软件建立使用加权回归（权由日期和涨跌幅综合决定）的股票基本面指标、技术指标对相对收益率的多因子模型，并且引入支持向量机作为风控，最终获得了一个收益较好的量化投资模型。
分类： 数学 >> 统计和概率 提交时间： 2024-02-04
摘要： The three frameworks for theories of consciousness taken most seriously by neuroscientists are that consciousness is a biological state of the brain,the global workspace perspective,and the perspective of higher state.Consciousness is discussed from viewpoint of theory of Entropypartition of complex system in present article. Human brains system self-organizably andadaptively implements partition 、 aggregation and integration, and consciousness emerges.The Gibss representation of consciousness is proved and That consciousness originates from quantum mechanical processes of brain activity is explained by means of SW entropy
分类： 数学 >> 计算数学 分类： 信息科学与系统科学 >> 信息科学与系统科学基础学科 提交时间： 2020-03-16
摘要： 针对目前大多数的低秩张量填充(LRTC)模型存在过度稀疏而导致数据的细微特征被忽略的现象, 本文借助框架变换和低秩矩阵分解, 提出了一个基于近似稀疏的低秩张量填充(AS-LRTC) 模型, 进一步设计了块逐次上界极小化(BSUM) 算法求解该模型. 在一定条件下可以证明该算法的收敛性, 大量的实验结果表明本文提出的算法比现有一些经典算法有明显的优势.
分类： 数学 >> 数学（综合） 提交时间： 2020-02-18
摘要： 2019年12月，新型冠状病毒肺炎(NCP，又称2019-nCoV)疫情从武汉开始爆发,几天内迅速传播到全国乃至海外，对我国的工农业生产和人民生活产生了重要影响。科学有效掌控疫情发展对疫情防控至关重要。本文基于中国卫健委及湖北省卫健委每日公布的累计确诊数，采用逻辑斯蒂模型对数据进行了拟合，以期给该疾病的防控治提供科学依据。通过公布的疫情数据，我们反演了模型的参数，进而有效地模拟了目前疫情的发展，并预测了疫情未来的趋势。我们预测，湖北省疫情还要持续至少2周，而在全国其他地区，疫情可望1周左右达到顶峰。
分类： 物理学 >> 基本粒子与场物理学 分类： 数学 >> 数学物理 提交时间： 2018-10-08
摘要： 本文系统地探讨了霍奇星算子与外微分算符作用于任意微分形式场时两者的一般组合规律。首先，找到了保持微分形式场的次不变的两个组合算符，并通过二者的线性组合得到了一个新算符。其次，当由任意数目的霍奇星算子与外微分算符进行组合时，作者导出了所有形式上彼此互异的组合算符的统一表达式，这些表达式由单个霍奇星算子与外微分算符以及二者的任选两个的非零组合构成。在此基础上，分析了所有算符之间的相互作用关系，并根据这些算符对微分形式的次的改变情况，对它们进行了具体分类。最后，作为一个应用，作者详细讨论了如何由次相同的微分形式的线性组合来构造电磁场的麦克斯韦方程。
分类： 数学 >> 统计和概率 提交时间： 2019-07-21
摘要： Based on the point of view of neuroethology and cognition-psychology, general frame of theory for intelligent systems is presented by means of principle of relative entropy minimizing in this paper. Cream of the general frame of theory is to present and to prove basic principle of intelligent systems: entropy increases or decreases together with intelligence in the intelligent systems. The basic principle is of momentous theoretical significance and practical significance .From the basic principle can not only derive two kind of learning algorithms (statistical simulating annealing algorithms and annealing algorithms of mean-field theory approximation) for training large kinds of stochastic neural networks,but also can thoroughly dispel misgivings created by second law of thermodynamics on 'peoplespsychology ,hence make one be fully confident of facing life.Because of Human society, natural world, and even universe all are intelligent systems.
分类： 数学 >> 计算数学 提交时间： 2019-04-10
摘要： 本文提出一个名为接圆回归的点击率预测新方法，尝试替代常用的因子分解机(FM)。接圆回归用超平面拼接出一个封闭凸多面体，圈出正样本，有直观的几何解释， 能从任意初始值一次收敛到全局最优解。 拟合出来的曲面Lipschitz连续，变化平缓。在人工设计的星环集、双堆集、双月集上，接圆回归的分类准确性、解释性、平滑性全面超过FM。在同量级参数量、计算量 的条件下，接圆回归在Avazu集和Criteo集上的AUC超过FM。
分类： 数学 >> 统计和概率 提交时间： 2018-11-07
摘要： Abstract. In studying of a class of random neural network, some of relative researchers have proposed Markov model of neural network. Wherein Markov property of the neural network is based on “assuming”. To reveal mechanism of generating of Markov property in neural network, it is studied how infinite-dimensional random neural network (IDRNN) forms inner Markov representation of environment information in this paper.Because of equivalence between markov property and Gibbsian our conclusion is that knowledge is eventually expressed by extreme Gibbs probability measure—ergodic Gibbs probability measure in IDRNN. This conclusion is also applicable to quantum mechanical level of IDRNN. Hence one can see “ concept “- “ consciousness” is generated at particle(ion) level in the brain and is experienced at the level of the neurons; We have discussed also ergodicity of IDRNN with random neural potential.
分类： 数学 >> 数学物理 提交时间： 2019-11-23
摘要： The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of 4th order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity of 3th order 2 dimensional (3 dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th order tensors, the analytically sufficient conditions of copositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for $\mathbb{Z}_3$ scalar dark matter.
分类： 数学 >> 应用数学 提交时间： 2016-07-07
摘要： 自博弈论中有趣的海盗分金问题（Pirate Game(PG)）提出以来，其在理论分析上，仅摘要：自博弈论中有趣的海盗分金问题（Pirate Game(PG)）提出以来，其在理论分析上，仅限于逆向递推法和数列递推法。本文首先借鉴这两种方法建立一阶差分模型；而后，考虑到每个海盗不是绝对理性的，等级高的海盗需要依赖等级低一级的海盗的决策而做出最优决策，建立二阶时滞差分模型，在数学原理上对 PG 做深入分析：当τ= 0 时，与实际情况偏差较大；当时滞量 τ=1 时，模型的解和一阶差分模型的解一致，即在现实生活中也存在着做决策时直接咨询自己的第一副手的社会群体。从而，在现代分析方法的层次上，本文给出一个 PG 的新的合理的数学解释。
分类： 数学 >> 控制和优化 提交时间： 2019-08-30
摘要： In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are 4th order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of 4th order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for 4th order 2 dimensional symmetric tensors. For 4th order 3 dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) cpositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for 4th order 2 dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for 4th order 2 dimensional symmetric tensors. Finally, we apply these results to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson.
分类： 数学 >> 建模与仿真 提交时间： 2019-10-23
摘要： Radiation symmetry evaluation is critical to the laser driven Inertial Confinement Fusion (ICF), which is usually done by solving a view-factor equation model. The model is nonlinear, and the number of equations can be very large when the size of discrete mesh element is very small to achieve a prescribed accuracy, which may lead to an intensive equation solving process. In this paper, an efficient radiation symmetry analysis approach based on sparse representation is presented, in which, 1) the Spherical harmonics, annular Zernike polynomials and Legendre-Fourier polynomials are employed to sparsely represent the radiation flux on the capsule and cylindrical cavity, and the nonlinear energy equilibrium equations are transformed into the equations with sparse coefficients, which means there are many redundant equations, 2) only a few equations are selected to recover such sparse coefficients with Latin hypercube sampling, 3) a Conjugate Gradient Subspace Thresholding Pursuit (CGSTP) algorithm is then given to rapidly obtain such sparse coefficients equation with as few iterations as possible. Finally, the proposed method is validated with two experiment targets for Shenguang II and Shenguang III laser facility in China. The results show that only one tenth of computation time is required to solve one tenth of equations to achieve the radiation flux with comparable accuracy. Further more, the solution is much more efficient as the size of discrete mesh element decreases, in which, only 1.2% computation time is required to obtain the accurate result.
分类： 数学 >> 数学（综合） 提交时间： 2022-06-30
摘要： This paper discusses the properties the spaces of fuzzy sets in a metric space?equipped with the endograph metric and the sendograph metric, respectively.?We fist give some relations among the endograph metric, the sendograph?metric and the -convergence, and then investigate the level characterizations?of the endograph metric and the -convergence. By using the above results,?we give some relations among the endograph metric, the sendograph metric,?the supremum metric and the dp* metric. On the basis of the above results,?we present the characterizations of total boundedness, relative compactness?and compactness in the space of compact positive -cuts fuzzy sets equipped?with the endograph metric, and in the space of compact support fuzzy sets?equipped with the sendograph metric, respectively. Furthermore, we give?completions of these metric spaces, respectively.
分类： 数学 >> 计算数学 提交时间： 2018-03-22
摘要： 本文通过严格数学分析找出了逻辑回归过拟合的成因：边界样本的损失贡献比重大且随法向量增长而加速增大、边界样本分布散乱，顺便理清了正则项的作用机理。 利用过拟合机制，本文提出一种反拉方法，既能缓解过拟合，又能减少训练步数，在MNIST数据集上实现加速38.25倍，在CIFAR10数据集上实现加速5.61倍。
分类： 数学 >> 控制和优化 提交时间： 2020-06-16
摘要： Quantization is a popular technique to reduce communication in distributed optimization. Motivated by the classical work on inexact gradient descent (GD) \cite{bertsekas2000gradient}, we provide a general convergence analysis framework for inexact GD that is tailored for quantization schemes. We also propose a quantization scheme Double Encoding and Error Diminishing (DEED). DEED can achieve small communication complexity in three settings: frequent-communication large-memory, frequent-communication small-memory, and infrequent-communication (e.g. federated learning). More specifically, in the frequent-communication large-memory setting, DEED can be easily combined with Nesterov's method, so that the total number of bits required is $ \tilde{O}( \sqrt{\kappa} \log 1/\epsilon )$, where $\tilde{O}$ hides numerical constant and $\log \kappa $ factors. In the frequent-communication small-memory setting, DEED combined with SGD only requires $\tilde{O}( \kappa \log 1/\epsilon)$ number of bits in the interpolation regime. In the infrequent communication setting, DEED combined with Federated averaging requires a smaller total number of bits than Federated Averaging. All these algorithms converge at the same rate as their non-quantized versions, while using a smaller number of bits.
点击量
待评议
点击量
下载量
评论
